Universe 9599 from The Wolfram Physics Project

10 steps

wm9599`wm9599`

signature

3₂→5₂

rule

{{{1, 2}, {1, 3}, {1, 4}} -> {{5, 6}, {5, 6}, {5, 2}, {3, 2}, {4, 3}}}

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Basic Evolution

Basic evolution:

[◼]	WolframModel

[{{{1,2},{1,3},{1,4}}{{5,6},{5,6},{5,2},{3,2},{4,3}}},{{1,1},{1,1},{1,1}},6,"StatesPlotsList"]

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

Event-by-event evolution:

[◼]	WolframModel

[{{{1,2},{1,3},{1,4}}{{5,6},{5,6},{5,2},{3,2},{4,3}}},{{1,1},{1,1},{1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"]

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

Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2},{1,3},{1,4}}{{5,6},{5,6},{5,2},{3,2},{4,3}}},{{1,1},{1,1},{1,1}},24,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-6-y.[n.]+y.[1+n.]-2y.[3+n.]+y.[5+n.]0,y.[1]1,y.[2]3,y.[3]4,y.[4]7,y.[5]11,y.[6]18,y.[7]27,y.[8]39,y.[9]55[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},-11n.+(2-n.)y.[n.]+(-4+n.)y.[1+n.]+2y.[2+n.]+(4-2n.)y.[3+n.]-4y.[4+n.]+(-2+n.)y.[5+n.]+2y.[6+n.]0,y.[1]3,y.[2]5,y.[3]7,y.[4]11,y.[5]17,y.[6]27[t]

Result after

generations:

WolframModel[

]

["FinalStatePlot"]

Causal Graph

Causal graph:

WolframModel[

]

"CausalGraph",

Rule[

]



Layered rendering:

WolframModel[

]

["LayeredCausalGraph"]

Causal graph distance matrix:

MatrixPlotTransposeGraphDistanceMatrix

WolframModel[

]

["CausalGraph"],



Final State Properties

Hypergraph adjacency matrix:

MatrixPlotAdjacencyMatrix@CatenateMapUndirectedEdge@@@Subsets[#,{2}]&,

WolframModel[

]

["FinalState"],



Vertex degree distribution:

HistogramValuesCountsCatenateUnion/@

WolframModel[

]

["FinalState"],



Neighborhood volumes (ignoring directedness of connections):

volumes=

[◼]	RaggedMeanAround

Values

[◼]	HypergraphNeighborhoodVolumes



WolframModel[

]

["FinalState"],All,Automatic;

ListLogLogPlotvolumes,



Effective dimension versus radius:

ListLinePlot

[◼]	LogDifferences

[volumes],

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Successive neighborhood balls around a random vertex:

[◼]	HypergraphNeighborhoods



WolframModel[

]

["FinalState"],4

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

Distance matrix:

distanceMatrix=GraphDistanceMatrixUndirectedGraph

[◼]	HypergraphToGraph



WolframModel[

]

["FinalState"];

MatrixPlotExp[-(distanceMatrix/.0None)],



Distribution of distances in the graph:

HistogramFlatten[distanceMatrix],

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Spreading of Effects

Causal graph adjacency matrix:

MatrixPlotAdjacencyMatrix

WolframModel[

]

["CausalGraph"],



Neighborhood volumes in causal graph:

ListLogLogPlotValues

[◼]	GraphNeighborhoodVolumes



WolframModel[

]

["CausalGraph"],{1},



Other Evolution Orders

Random evolutions:

[◼]	WolframModel

[{{{1,2},{1,3},{1,4}}{{5,6},{5,6},{5,2},{3,2},{4,3}}},{{1,1},{1,1},{1,1}},<|"MaxEvents"84|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2},{1,3},{1,4}}{{5,6},{5,6},{5,2},{3,2},{4,3}}},{{1,1},{1,1},{1,1}},<|"MaxEvents"84|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

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